If the light switch has a ground screw on it (usually green and at the bottom of the switch), connect it now. Single pole switch wiring. Second twist the two white. Nov The procedure is not unlike wiring multiple lights to a single switch.
Conversely, you can connect the switch for a new light fixture to a nearby. The neutral wire provides power to the light switch, even when the lights are off.
A neutral wire does not. Jul You have the right idea. You understand that a wire going into a backstab right next to the screw is the same as going to the screw.
I almost had my daughter wire this light switch but then imagined what my wife would say! If your switches look old and grimy you may need to replace them.